where
\(\ell _{\rm mar}\)  is per (REF ),
and \(S\stackrel{.}{=}\lbrace (x_{i},y_{i})\rbrace _{i=1}^{N}\stackrel{\text{i.i.d.}}{\sim }\mathbb {P}^{N}\)  is a training sample from the joint distribution \(\mathbb {P}\) .
Furthermore, \(\lambda \ge 0\)  controls the trade-off between logit margin
(promoted by \(\ell _{\rm mar}\) )
and embedding margin (encouraged by \(\Omega _{\rm pull}\) ).
Inspired by objectives in metric learning [1]},
we shall consider
\(\Omega _{\rm pull}( x, y ) &\stackrel{.}{=}\log \left[ 1 +\sum \nolimits _{x^+\in S_y \backslash \lbrace x\rbrace } e^{\Vert  \Phi ( x ) - \Phi ( x^+) \Vert _2^2 - \alpha _y} \right],\) 
